Simultaneous kinematic and hand-eye calibration

ABSTRACT

Described are machine vision systems and methods for simultaneous kinematic and hand-eye calibration. A machine vision system includes a robot or motion stage and a camera in communication with a control system. The control system is configured to move the robot or motion stage to poses, and for each pose: capture an image of calibration target features and robot joint angles or motion stage encoder counts. The control system is configured to obtain initial values for robot or motion stage calibration parameters, and determine initial values for hand-eye calibration parameters based on the initial values for the robot or motion stage calibration parameters, the image, and joint angles or encoder counts. The control system is configured to determine final values for the hand-eye calibration parameters and robot or motion stage calibration parameters by refining the hand-eye calibration parameters and robot or motion stage calibration parameters to minimize a cost function.

FIELD OF THE TECHNOLOGY

The present technology relates generally to machine vision systems and,more specifically, to calibrating machine vision systems bysimultaneously refining kinematic chain of robots/motion stages andhand-eye calibration parameters.

BACKGROUND

In machine vision systems, one or more cameras can be used to performvision system processes on an object or surface within an imaged scene.These processes can include inspection, alignment, and/or a variety ofother tasks. The images captured by the one or more cameras can beprocessed by the machine vision system to determine information aboutfeatures within the imaged scene, such as features' real-worldlocations, poses, etc. In some applications, a machine vision system caninclude a robot, motion stage, or other device whose pose and movementis controlled by the machine vision system (e.g., Vision Guided Robot(VGR) applications). For example, the machine vision system can analyzethe images captured by the one or more cameras to determine how to movethe robot or motion stage to move or interact with objects in the imagedscene. In some applications, the machine vision system can be calibratedto allow the machine vision system to perform vision tasks withincreased accuracy and reliability.

SUMMARY

The technology described herein can improve the accuracy and precisionof existing machine vision systems by improving the kinematics modellingof the robot/motion stage and the calibration of the machine visionsystem.

In one aspect, there is a machine vision system. The machine visionsystem includes a robot. The machine vision system includes a camera.The machine vision system includes a control system in communicationwith the robot and the camera. The control system is configured to movethe robot to a plurality of poses, and for each pose of the plurality ofposes: capture, with the camera, an image of one or more features on acalibration target and capture a plurality of robot joint angles. Thecontrol system is configured to obtain a plurality of initial values fora plurality of robot calibration parameters. The control system isconfigured to determine a plurality of initial values for a plurality ofhand-eye calibration parameters based on the plurality of initial valuesfor the plurality of robot calibration parameters, and the image and theplurality of robot joint angles captured for each of the plurality ofposes. The control system is configured to determine a plurality offinal values for the plurality of hand-eye calibration parameters and aplurality of final values for the robot calibration parameters byrefining one or more of the plurality of hand-eye calibration parametersand one or more of the plurality of robot calibration parameters tominimize a cost function.

In some embodiments, the control system is further configured to use theplurality of final values for the plurality of hand-eye calibrationparameters and the plurality of final values for the robot calibrationparameters for a vision guided robot application. In some embodiments,the control system is further configured to move the robot using theplurality of final values for the robot calibration parameters.

In some embodiments, the cost function measures, for each pose of theplurality of poses, a difference between an observed location of afeature in the image captured for the pose and an expected location ofthe feature, the expected location determined based on a first pluralityof values for the plurality of robot calibration parameters, a secondplurality of values for the plurality of hand-eye calibrationparameters, and the plurality of robot joint angles captured for thepose. In some embodiments, the cost function measures, for each pose ofthe plurality of poses, a difference between a composite transformationand an identity transformation, the composite transformation being acomposition of a first transformation from a first coordinate space to asecond coordinate space and a second transformation from the secondcoordinate space to the first coordinate space, the first transformationand the second transformation determined based on a first plurality ofvalues for the plurality of robot calibration parameters, a secondplurality of values for the plurality of hand-eye calibrationparameters, the plurality of observed features of the calibration targetfor the pose, and the plurality of robot joint angles captured for thepose. In some embodiments, the cost function measures, for each pose ofthe plurality of poses, a difference between a robot joint angle of theplurality of robot joint angles captured for the pose and an estimatedjoint angle for the pose, the estimated joint angle determined based ona first plurality of values for the plurality of robot calibrationparameters, a second plurality of values for the plurality of hand-eyecalibration parameters, and the plurality of observed features of thecalibration target for the pose.

In some embodiments, the control system is further configured tominimize the cost function using non-linear least squares. In someembodiments, the control system is configured to refine less than all ofthe plurality of hand-eye calibration parameters and less than all ofthe plurality of robot calibration parameters. In some embodiments, theplurality of robot calibration parameters includes Denavit-Hartenbergparameters for the robot.

In another aspect, there is a machine vision system-implementedcalibration method. The method includes moving, by a control system, arobot to a plurality of poses, and for each pose of the plurality ofposes: capturing, by a camera, an image of one or more features on acalibration target and capturing, by the control system, a plurality ofrobot joint angles. The method includes obtaining, by the controlsystem, a plurality of initial values for a plurality of robotcalibration parameters. The method includes determining, by the controlsystem, a plurality of initial values for a plurality of hand-eyecalibration parameters based on the plurality of initial values for theplurality of robot calibration parameters, and the image and theplurality of robot joint angles captured for each of the plurality ofposes. The method includes determining, by the control system, aplurality of final values for the plurality of hand-eye calibrationparameters and a plurality of final values for the plurality of robotcalibration parameters by refining one or more of the plurality ofhand-eye calibration parameters and one or more of the plurality ofrobot calibration parameters to minimize a cost function.

In some embodiments, the cost function measures, for each pose of theplurality of poses, a difference between an observed location of afeature in the image captured for the pose and an expected location ofthe feature, the expected location determined based on a first pluralityof values for the plurality of robot calibration parameters, a secondplurality of values for the plurality of hand-eye calibrationparameters, and the plurality of robot joint angles captured for thepose. In some embodiments, the cost function measures, for each pose ofthe plurality of poses, a difference between a composite transformationand an identity transformation, the composite transformation being acomposition of a first transformation from a first coordinate space to asecond coordinate space and a second transformation from the secondcoordinate space to the first coordinate space, the first transformationand the second transformation determined based on a first plurality ofvalues for the plurality of robot calibration parameters, a secondplurality of values for the plurality of hand-eye calibrationparameters, the plurality of observed features of the calibration targetfor the pose, and the plurality of robot joint angles captured for thepose. In some embodiments, the cost function measures, for each pose ofthe plurality of poses, a difference between a robot joint angle of theplurality of robot joint angles captured for the pose and an estimatedjoint angle for the pose, the estimated joint angle determined based ona first plurality of values for the plurality of robot calibrationparameters, a second plurality of values for the plurality of hand-eyecalibration parameters, and the plurality of observed features of thecalibration target for the pose.

In some embodiments, the method includes minimizing the cost functionusing non-linear least squares. In some embodiments, the method includesrefining less than all of the plurality of hand-eye calibrationparameters and less than all of the plurality of robot calibrationparameters. In some embodiments, the plurality of robot calibrationparameters includes Denavit-Hartenberg parameters for the robot.

In another aspect, there is a machine vision system. The machine visionsystem includes a motion stage. The machine vision system includes acamera. The machine vision system includes a control system incommunication with the motion stage and the camera. The control systemis configured to move the motion stage to a plurality of poses, and foreach pose of the plurality of poses: capture, with the camera, an imageof one or more features on a calibration target and capture a pluralityof encoder counts for a plurality of actuators of the motion stage. Thecontrol system is configured to obtain a plurality of initial values fora plurality of motion stage calibration parameters. The control systemis configured to determine a plurality of initial values for a pluralityof hand-eye calibration parameters based on the plurality of initialvalues for the plurality of motion stage calibration parameters, and theimage and the plurality of encoder counts captured for each of theplurality of poses. The control system is configured to determine aplurality of final values for the plurality of hand-eye calibrationparameters and a plurality of final values for the motion stagecalibration parameters by refining one or more of the plurality ofhand-eye calibration parameters and one or more of the plurality ofmotion stage calibration parameters to minimize a cost function.

In some embodiments, the control system is further configured to use theplurality of final values for the plurality of hand-eye calibrationparameters and the plurality of final values for the motion stagecalibration parameters for a vision guided motion stage application. Insome embodiments, the control system is further configured to move themotion stage using the plurality of final values for the motion stagecalibration parameters.

In some embodiments, the cost function measures, for each pose of theplurality of poses, a difference between an observed location of afeature in the image captured for the pose and an expected location ofthe feature, the expected location determined based on a first pluralityof values for the plurality of motion stage calibration parameters, asecond plurality of values for the plurality of hand-eye calibrationparameters, and the plurality of encoder counts captured for the pose.In some embodiments, the cost function measures, for each pose of theplurality of poses, a difference between an encoder count of theplurality of encoder counts captured for the pose and an estimatedencoder count for the pose, the estimated encoder count determined basedon a first plurality of values for the plurality of motion stagecalibration parameters, a second plurality of values for the pluralityof hand-eye calibration parameters, and the plurality of observedfeatures of the calibration target for the pose.

In some embodiments, the control system is further configured tominimize the cost function using non-linear least squares. In someembodiments, the control system is configured to refine less than all ofthe plurality of hand-eye calibration parameters and less than all ofthe plurality of motion stage calibration parameters. In someembodiments, the plurality of motion stage calibration parametersincludes one or more of roller center position, roller radius,direction, step size, home encoder count, and striker plate's directionfor an actuator.

In another aspect, there is a machine vision system-implementedcalibration method. The method includes moving, by a control system, amotion stage to a plurality of poses, and for each pose of the pluralityof poses: capture, by a camera, an image of one or more features on acalibration target; and capturing, by the control system, a plurality ofencoder counts for a plurality of actuators of the motion stage. Themethod includes obtaining, by the control system, a plurality of initialvalues for a plurality of motion stage calibration parameters. Themethod includes determining, by the control system, a plurality ofinitial values for a plurality of hand-eye calibration parameters basedon the plurality of initial values for the plurality of motion stagecalibration parameters, and the image and the plurality of encodercounts captured for each of the plurality of poses. The method includesdetermining, by the control system, a plurality of final values for theplurality of hand-eye calibration parameters and a plurality of finalvalues for the motion stage calibration parameters by refining one ormore of the plurality of hand-eye calibration parameters and one or moreof the plurality of motion stage calibration parameters to minimize acost function.

In some embodiments, the cost function measures, for each pose of theplurality of poses, a difference between an observed location of afeature in the image captured for the pose and an expected location ofthe feature, the expected location determined based on a first pluralityof values for the plurality of motion stage calibration parameters, asecond plurality of values for the plurality of hand-eye calibrationparameters, and the plurality of encoder counts captured for the pose.In some embodiments, the cost function measures, for each pose of theplurality of poses, a difference between an encoder count of theplurality of encoder counts captured for the pose and an estimatedencoder count for the pose, the estimated encoder count determined basedon a first plurality of values for the plurality of motion stagecalibration parameters, a second plurality of values for the pluralityof hand-eye calibration parameters, and the plurality of observedfeatures of the calibration target for the pose.

In some embodiments, the method includes minimizing the cost functionusing non-linear least squares. In some embodiments, the method includesrefining less than all of the plurality of hand-eye calibrationparameters and less than all of the plurality of motion stagecalibration parameters. In some embodiments, the plurality of motionstage calibration parameters includes one or more of roller centerposition, roller radius, direction, step size, home encoder count, andstriker plate's direction for an actuator.

Other aspects and advantages of the technology will become apparent fromthe following detailed description, taken in conjunction with theaccompanying drawings, illustrating the principles of the technology byway of example only.

BRIEF DESCRIPTION OF THE DRAWINGS

The foregoing and other objects, features, and advantages of the presenttechnology, as well as the technology itself, will be more fullyunderstood from the following description of various embodiments, whenread together with the accompanying drawings, in which:

FIG. 1 illustrates an exemplary machine vision system.

FIG. 2 illustrates an exemplary machine vision system.

FIG. 3 depicts a calibration scheme in accordance with the technology.

FIG. 4 depicts a flowchart of a method of calibrating a machine visionsystem in accordance with the technology.

FIG. 5 depicts a calibration scheme in accordance with the technology.

DETAILED DESCRIPTION

Precisely calibrating machine vision systems for VGR applications can becritical. Existing approaches to calibrating such machine vision systems(e.g., machine vision systems with a robot, motion stage, or otherdevice) can result in machine vision systems that do not have therequisite accuracy for many applications. For example, in many cases,calibrating the machine vision system based on the kinematic calibrationparameter values (e.g., robot calibration parameter values or motionstage calibration parameter values) provided by robot or motion stagemanufacturers can lead to inadequate accuracy of the machine visionsystem. The present technology can improve the accuracy and precision ofmachine vision systems for VGR applications by using efficientcalibration techniques to refine kinematic calibration parameters andhand-eye calibration parameters. The technology can be used to determinemore accurate calibration parameter values, including the hand-eyecalibration parameters and kinematic calibration parameters, in a singlerefinement calculation based on measurements determined by the machinevision system. Beneficially, the technology can increase the accuracy ofthe machine vision systems through improved calibration without, forexample, requiring additional calibration targets, additional cameras,or external measurement equipment.

I. Machine Vision Systems

FIG. 1 illustrates exemplary machine vision system 100. Machine visionsystem 100 can be used, for example, for VGR applications. Machinevision system 100 includes robot 105 with a camera 110 mounted thereon,and control system 115. FIG. 1 illustrates a moving camera configuration(e.g., camera 110 is mounted on the arm of robot 105). Still referringto FIG. 1, calibration target 120 having features 123 is shown. Camera110 can be an area-scan camera including a two-dimensional CCD camerasensor, a two-dimensional CMOS camera sensor or any other type of camerasensor for generating images. Control system 115 can be any processingdevice (e.g., embedded machine vision processor, computing device,etc.).

Control system 115 is in communication with robot 105 and camera 110.Control system 115 can receive image data from camera 110 and controlthe pose of robot 105. In some embodiments, Control system 115 can be apart of a standalone computing device. In some embodiments, controlsystem 115 can be a part of robot 105. In some embodiments, controlsystem 115 can be a part of camera 110. In operation, control system 115can manipulate the pose of robot 105, e.g., based on analysis of imagedata from camera 110. For simplicity, control system 115 is illustratedas a single component. In some embodiments, the control system caninclude a motion controller (e.g., a robot controller) and a machinevision processor working in concert. In some embodiments, the motioncontroller can be the machine vision system master. For example, themotion controller can communicate with and direct the actions of themachine vision processor. The motion controller can control the pose andmovement of the robot and cause the machine vision processor to acquireimages. The motion controller can provide pose information to themachine vision processor and cause the machine vision processor toperform the calibration described herein. In some embodiments, themachine vision processor can be the machine vision system master. Forexample, the machine vision processor can communicate with and directthe actions of the motion controller. The machine vision processor cancause the motion controller to control the pose and movement of therobot, and provide pose information to the machine vision processor. Themachine vision processor can acquire images and perform the calibrationdescribed herein. In some embodiments, the motion controller and machinevision controller can be integrated. For example, one or more processorcores of a control system can control robot motion and one or moreprocessor cores of the control system can perform machine visionprocessing such as calibration.

In accordance with the technology, the machine vision system 100 can becalibrated. As will be described in greater detail below, system 100 canbe calibrated to permit transformation of coordinates between the imagecoordinate space of camera 110, the coordinate spaces of the robot 105,and the coordinate space of calibration target 120. Using thecalibration, control system 115 can direct robot hand 160 to preciselocations in the coordinate space of calibration target 120 or in therobot base coordinate space. Control system 115 can further determinethe location of objects observed in image data from camera 110 by usingthe calibration and information about the angles of the joints of robot105. Beneficially, the calibration permits machine vision system tocontrol the motion of robot hand 160 and use it to interact with and/ormanipulate real-world objects (e.g., in the coordinate space ofcalibration target 120).

FIG. 2 illustrates exemplary machine vision system 200. Machine visionsystem 200 can be used, for example, for VGR applications. Machinevision system 200 includes motion stage 205, camera 210, and controlsystem 215. As illustrated, camera 210 can be mounted above motion stage205 to image a top surface of motion stage 205. In the illustratedembodiment, camera 210 is mounted in a fixed way relative to base 208 ofmotion stage 205 (e.g., table 209 of motion stage 205 can move relativeto camera 210). Camera 210 can be an area-scan camera including atwo-dimensional CCD camera sensor, a two-dimensional CMOS camera sensoror any other type of camera sensor for generating images. Control system215 can be any processing device (e.g., embedded machine visionprocessor, computing device, etc.). Still referring to FIG. 2,calibration target 220 having features 223 is shown.

Control system 215 is in communication with motion stage 205 and camera210. Control system can receive image data from camera 210 and controlthe pose of motion stage 205. In some embodiments, control system 215can be a part of a standalone computing device. In some embodiments,control system 215 can be a part of motion stage 205. In someembodiments, control system 215 can be a part of camera 210. Inoperation, control system 215 can change the pose of motion stage 205,e.g., based on analysis of image data from camera 210. For simplicity,control system 215 is illustrated as a single component. In someembodiments, the control system can include a motion controller (e.g., amotion stage controller) and a machine vision processor working inconcert. In some embodiments, the motion controller can be the machinevision system master. For example, the motion controller can communicatewith and direct the actions of the machine vision processor. The motioncontroller can control the pose and movement of the motion stage andcause the machine vision processor to acquire images. The motioncontroller can provide pose information to the machine vision processorand cause the machine vision processor to perform the calibrationdescribed herein. In some embodiments, the machine vision processor canbe the machine vision system master. For example, the machine visionprocessor can communicate with and direct the actions of the motioncontroller. The machine vision processor can cause the motion controllerto control the pose and movement of the motion stage, and provide poseinformation to the machine vision processor. The machine visionprocessor can acquire images and perform the calibration describedherein. In some embodiments, the motion controller and machine visioncontroller can be integrated. For example, one or more processor coresof a control system can control motion stage motion and one or moreprocessor cores of the control system can perform machine visionprocessing such as calibration.

In accordance with the technology, machine vision system 200 can becalibrated. As will be described in greater detail below, system 200 canbe calibrated to permit transformation of coordinates between the imagecoordinate space of camera 210, the coordinate spaces of motion stage205, and the coordinate space of calibration target 220. Using thecalibration, control system 215 can translate and/or rotate motion stage205 to precise poses in the coordinate space of calibration target 220or in the coordinate space of motion stage 205. Control system 215 canfurther determine the location of objects observed in image data fromcamera 210 by using the calibration and information about the actuatorsof motion stage 105. Beneficially, the calibration permits machinevision system 200 to control the motion of motion stage 205 and use itto move real-world objects on its surface (e.g., in the coordinate spaceof calibration target 220).

It should be appreciated that the illustrated embodiments are merelyexemplary machine vision system configurations. In some embodiments, themachine vision system can include other kinds of robots, other kinds ofmotion stages, or other devices whose movement can be controlled by themachine vision system. In some embodiments, the camera can be mounted tothe robot or motion stage, or a fixture independent of the robot ormotion stage (e.g., stationary camera scenarios and/or moving camerascenarios). In some embodiments, more than one camera can be used. Insome embodiments, the robot or motion stage can interact with multipleworkspaces.

II. Calibration

The technology can facilitate improved accuracy of machine visionsystems by providing an efficient technique for refining calibrationparameter values. Generally, calibration parameters can include hand-eyecalibration parameters, as are well known in the art. In the case ofmachine vision systems with robots, calibration parameters can includerobot calibration parameters. In the case of machine vision systems withmotion stages, calibration parameters can include motion stagecalibration parameters. Robot calibration parameters and/or motion stagecalibration parameters can be referred to as kinematic calibrationparameters. For robots, robot calibration parameters can include theDenavit-Hartenberg parameters (D-H parameters) used for describing,e.g., the links and joints of robots. As another example, UVW motionstages are motion stages that can, for example, include two actuatorsmoving in the X direction, and one actuator moving in Y direction. ForUVW motion stages, motion stage calibration parameters can include, foreach actuator, the roller's center position, the roller's radius, theactuator's direction, the actuator's step size, the actuator's homeencoder count, and the striker plate's direction. As still anotherexample, XY Theta motion stages are motion stages that can, for example,include an actuator for linear translation along the X axis, an actuatorfor linear translation along the Y axis, and a theta actuator providingrotation. For XY Theta motion stages, motion stage calibrationparameters can include, direction and step size for each of the X and Yactuators, and the roller's center position and radius, the actuator'sdirection and step size, the striker plate's direction for the thetaactuator. More generally, the technology can be used for calibration ofmotion devices that can be modeled geometrically. For example, thetechnology can be used for calibration of motion devices whose geometrycan be represented with calibration parameter values.

A. Calibration for Machine Vision Systems with Robots

The technology can refine calibration parameter values by minimizing theinaccuracies caused by robots' variance from their specifications andother conditions. In an exemplary embodiment of the technology, a robot(e.g., robot 105) is moved to a plurality of poses, and for each posethe machine vision system captures an image (e.g., via camera 110) of acalibration target (e.g., calibration target 120) and the robot's jointangles at that pose. Initial calibration parameter values can bedetermined. For example, initial robot calibration parameter values canbe taken from the robot's specification. Initial hand-eye calibrationparameter values can be determined using the captured images and theinitial robot calibration parameter values. Calibration functionalityfor determining the initial hand-eye calibration parameter values iscommercially available, such as in the Cognex Vision Library® producedby Cognex Corporation. One or more initial calibration parameter values,including one or more robot calibration parameter values and one or morehand-eye calibration parameters, can then be refined to determine finalcalibration parameter values. For example, by using a nonlinearoptimization method to minimize the overall discrepancy between therobot motion, which can be determined using the robot calibrationparameters and the joint angles, and the motion observed by the machinevision system. The final calibration parameter values can then be usedby the machine vision system to operate the robot during runtime. Forexample, the final robot calibration parameter values can be used tocontrol the robot more accurately. The final hand-eye calibrationparameter values can further improve the performance of the machinevision system at run time.

FIG. 3 depicts calibration scheme 300 in accordance with the technology.In some embodiments, the calibration scheme can be used for movingcamera configurations. For example, calibration scheme 300 can be usedfor machine vision system 100 of FIG. 1. In FIG. 3, the ovals representcoordinate spaces. FIG. 3 includes CalPlate3D coordinate space 305,RobotBase3D coordinate space 310, Joint1 coordinate space 315, Joint2coordinate space 320, Joint3 coordinate space 325, Joint4 coordinatespace 330, Joint5 coordinate space 335, Joint6 coordinate space 340,Hand3D coordinate space 345, Camera3D coordinate space 352, and Raw2Dcoordinate space 355. Arrows between ovals represent transformationsbetween the illustrated coordinate spaces. The calibration parametervalues used for the transformations can be determined and refined, asdescribed with respect to the illustrative calibration methods below.

In the illustrated example, CalPlate3D coordinate space 305 can be thecoordinate space of calibration target 120, and can be defined by thetop surface of calibration target 120. RobotBase3D coordinate space 310can be the coordinate space of base 125 of robot 105. In someembodiments, RobotBase3D coordinate space 310 can be defined by therobot manufacturer. Joint1 coordinate space 315 can be the coordinatespace of joint 130 of robot 105. Joint2 coordinate space 320 can be thecoordinate space of joint 135 of robot 105. Joint3 coordinate space 325can be the coordinate space of joint 140 of robot 105. Joint4 coordinatespace 330 can be the coordinate space of joint 145 of robot 105. Joint5coordinate space 335 can be the coordinate space of joint 150 of robot105. Joint6 coordinate space 340 can be the coordinate space of joint155 of robot 105. Hand3D coordinate space 345 can be the coordinatespace of hand 160 of robot 105. In some embodiments, Hand3D coordinatespace 345 can be defined by the robot manufacturer. In some embodiments,Hand3D coordinate space 345 is a user defined offset from J6. Camera3Dcoordinate space 352 can be the coordinate space of camera 110. Theorigin of Camera3D coordinate space 352 can be at the center ofprojection with the z axis pointing out along the optical axis of thelens of camera 110. The x and y axes can be aligned with the rows andcolumns, respectively, of the camera sensor of camera 110. Raw2Dcoordinate space 355 can be a 2D pixel-based coordinate system definedby the rows and columns of the camera sensor of camera 110. The x axiscan point from left to right along the image rows, and the y axis canpoint down along the columns of the camera sensor of camera 110. Itshould be appreciated that coordinate spaces with names containing “3D”are three-dimensional spaces, and coordinate spaces with namescontaining “2D” are two-dimensional spaces.

The transformations between the coordinate spaces can be rigidtransformations (e.g., comprising a translation component and a rotationcomponent) and/or transformations based on the robot calibrationparameters of robot 105. For example, the transformations betweenCalPlate3D coordinate space 305 and RobotBase3D coordinate space 310,between RobotBase3D coordinate space 310 and Joint1 coordinate space315, between Hand3D coordinate space 345 and Camera3D coordinate space352, and between CalPlate3D coordinate space 305 and Camera3D coordinatespace 352, can be 3D rigid transformations. The transformations betweenJoint1 coordinate space 315 and Joint2 coordinate space 320, betweenJoint2 coordinate space 320 and Joint3 coordinate space 325, betweenJoint3 coordinate space 325 and Joint4 coordinate space 330, betweenJoint4 coordinate space 330 and Joint5 coordinate space 335, and betweenJoint5 coordinate space 335 and Joint6 coordinate space 340 can be basedon the robot calibration parameter values describing the joints andlinks of robot 105, and the corresponding joint angle values. In someembodiments, the transformations can be determined using aDenavit-Hartenberg matrix, where the robot parameters are d, θ, a, andalpha, as is well known in the art. The transformation from Joint6coordinate space 340 to Hand3D coordinate space 345 can be a rigidtransformation along with a variable rotational transform based on theangle value of Joint6 of robot 105. The transformation from CalPlate3Dcoordinate space 305 to Camera3D coordinate space 352, and thetransformation from Camera3D coordinate space 352 to Raw2D coordinatespace 355 can be based on a conventional camera calibration, as is wellknown in the art. As used herein, the notationCoordinateSpace1fromCoordinateSpace2 indicates the transformation fromCoordinateSpace2 to CoordinateSpace1. For example, Joint1Frompoint2denotes the transformation from Joint2 coordinate space 320 to Joint1coordinate space 315.

The present technology can be used to refine the calibration parametervalues used to form the transformations described above.

1. Capturing Calibration Data

FIG. 4 depicts flowchart 400 of a method of calibrating a machine visionsystem in accordance with the technology. The depicted method can beperformed by control system 115. At step 405, control system 115captures images and robot joint angles when the robot 105 is in aplurality of poses. At each pose, control system 115 causes camera 110to capture an image of at least a portion of calibration target 120 thatcontains one or more of features 122. Control system 115 furthercaptures the angle of each joint of robot 105 at the pose. For example,robot 105 can report the angle of each joint to control system 115.

2. Determining Initial Calibration Parameter Values

At step 410, control system 115 determines initial calibration parametervalues. The initial calibration parameter values can be the values usedto determine the transformations discussed with reference to FIG. 3prior to refinement. As will be described in greater detail below, thevalues of these calibrations parameters can be refined in accordancewith the present technology. In the illustrated example of FIG. 3,control system 115 can obtain the initial robot calibration parametervalues for robot 105 based on the specification of robot 105. Forexample, a robot manufacturer will typically provide these values. Usingthese initial calibration values and joint angles for robot 105 at aparticular pose, control system 115 can determine the followingtransformations for robot 105 at that pose: RobotBase3DFromJoint1,Joint1 FromJoint2, Joint2FromJoint3, Joint3FromJoint4, Joint4FromJoint5,Joint5FromJoint6, and Joint6FromHand3D. For example, Joint1FromJoint2,Joint2FromJoint3, Joint3FromJoint4, Joint4FromJoint5, Joint5FromJoint6can be determined using the Denavit-Hartenberg matrix based on the D-Hvalues provided by the robot specification and the joint angle values ofrobot 105 at the pose. RobotBase3DFromJoint1 can be determined based onthe robot specification (e.g., the dimensions of robot 105).Joint6FromHand3D can be determined based on the robot specification ofHand3D 160 of robot 105 and the joint angle value of Joint6.Joint6FromHand3D can provide the rigid transformation of robot hand 160in J6 340 (e.g., the Joint 6 coordinate system). Control system 115 canform the composite transformation RobotBase3DFromHand3D for a particularpose of robot 105 based on these transformations. For example, theequation below provides RobotBase3DFromHand3D:RobotBase3DFromHand3D=RobotBase3DFromJoint1*Joint1FromJoint2*Joint2FromJoint3*Joint3FromJoint4*Joint4FromJoint5*Joint5FromJoint6*Joint6FromHand3D

Control system 115 can perform a hand-eye calibration to determineinitial hand-eye calibration parameter values. For example, controlsystem can use the Cognex Vision Library to determine initial hand-eyecalibration parameter values based on the captured images and theRobotBase3DFromHand3D transformation for a plurality of poses, alongwith the Camera3DFromCalPlate3D transformation. As a result of thehand-eye calibration, control system 115 can determineCamera3DFromHand3D and RobotBase3DFromCalPlate3D. With the determinationof Camera3DFromHand3D and RobotBase3DFromCalPlate3D, along with thepreviously determined transformations, coordinates in any coordinatespace of FIG. 3 can be transformed into coordinates in any othercoordinate space of FIG. 3.

3. Refining Calibration Parameters

At step 415, control system 115 refines a plurality of the calibrationparameters to determine more accurate values for those calibrationparameters. To refine the calibration parameters, control system 115determines the calibration parameter values that minimize a costfunction. Techniques for minimizing the cost function and determiningfinal calibration parameter values can include non-linear least squares.One of skill in the art will appreciate that other techniques can beused.

Embodiments of the technology can use a variety of cost functions. Insome embodiments, the cost function can be the sum of the distancesbetween observed locations of features (e.g., features on calibrationtarget 120) and the expected locations of those features based on thetransformations discussed. In general, this can involve the machinevision system observing the location of a feature in a first coordinatespace (e.g., observing with camera 110) and applying a series oftransformations to map that feature through a plurality of othercoordinate spaces to the first coordinate space to calculate theexpected location of that feature based on the calibration parameters.If the calibration parameters are completely accurate, the observedlocation and the expected location will be the same. In practice, thereare typically some differences between the observed location and theexpected location. In some embodiments, the cost function measures thesedifferences for multiple features, multiple poses, and multiple images.For example, control system 115 can determine the location of aplurality of observed calibration target features in Raw2D coordinatespace 355 for each robot pose (ObservedFeatureRaw2D_(ij)). Controlsystem 115 can also determine the location of a plurality of mappedcalibration target features in Raw2D coordinate space 355 for each robotposeMappedFeatureRaw2D_(ij)=Raw2DFromCamera3D*CalPlate3DFromCamera3DAtPose_(i)Estimated⁻¹*CalibrationTargetFeature_(j)

-   -   where        CalPlate3DFromCamera3DAtPose_(i)Estimated=CalPlate3DFromRobotBase3D*RobotBase3DFromHand3DAtPose_(i)*Hand3DFromCamera3D    -   RobotBase3DFromHand3DAtPose_(i) is the estimated robot pose at        pose i using the joint angle values at pose i and the initial        calibration parameters values (or successively refined        calibration parameter values).        Control system 115 can then compute the distance between the        observed feature location and the mapped feature location. The        cost function can be defined as follows:

$\sum\limits_{\underset{{and}\mspace{14mu}{each}\mspace{14mu}{feature}\mspace{14mu} j}{{{For}\mspace{14mu}{each}\mspace{14mu}{camera}},{{each}\mspace{14mu}{pose}\mspace{14mu} i},}}\;( {{diatance}\begin{pmatrix}{{{ObservedFeatureRaw}\; 2\; D_{ij}},} \\{{MappedFeatureRaw}\; 2\; D_{ij}}\end{pmatrix}} )^{2}$In some embodiments, the cost function measures the changes of thelocation of the calibration plate features after mapping using thetransforms. For example, control system 115 can determine the locationof a plurality of features in CalPlate3D coordinate space 305. Controlsystem 115 can also map each feature location for the plurality featuresat each robot pose i of the plurality poses through the transformationCalPlate3DFromCalPlate3DAtPose_(i), where:CalPlate3DFromCalPlate3DAtPose_(i)=CalPlate3DFromRobotBase3D*RobotBase3DFromHand3DAtPose_(i)*Hand3DFromCamera3D*Camera3DFromCalPlate3DAtPose_(i)

-   -   Where RobotBase3DFromHand3DAtPose_(i) is the estimated robot        pose at pose i using the joint angle values at pose i and the        initial calibration parameters values (or successively refined        calibration parameter values).    -   Camera3DFromCalPlate3DAtPose_(i) is obtained by using the        observed features in Raw2D and camera calibration information.        Control system 115 can then compute the distance between the        feature location and the mapped feature location. The cost        function can be defined as follows:

$\sum\limits_{\underset{{and}\mspace{14mu}{each}\mspace{14mu}{feature}\mspace{14mu} j}{{{For}\mspace{14mu}{each}\mspace{14mu}{camera}},{{each}\mspace{14mu}{pose}\mspace{14mu} i},}}\;( {{diatance}\begin{pmatrix}{{CalPlate}\; 3\; D\;{FromCalPlate}\; 3\;{DAtPose}_{i}*} \\{{{featureCalPlate}\; 3\; D_{j}},{{featureCalPlate}\; 3\; D_{j}}}\end{pmatrix}} )^{2}$

In some embodiments, the cost function can be defined without mappingfeature points. If the calibration parameters are completely accurate,then CalPlate3DFromCalPlate3DAtPose_(i) would be an identitytransformation. Thus, the cost function can measure the differencebetween CalPlate3DFromCalPlate3DAtPose_(i) and the identitytransformation. In some embodiments, the cost function can be defined asfollows:

$\sum\limits_{{{For}\mspace{14mu}{each}\mspace{14mu}{camera}},{{each}\mspace{14mu}{pose}\mspace{14mu} i},}\;\begin{pmatrix}{{{CalPlate}\; 3\; D\;{fromCalPlate}\; 3\;{{DAtPose}_{i}.{translation}.{length}}} + {w*}} \\{{absolute}\mspace{14mu}{value}} \\( {{CalPlate}\; 3\;{DfromCalPlate}\; 3\;{{DAtPose}_{i}.{rotationAngle}}} )\end{pmatrix}^{2}$

-   -   Where:    -   CalPlate3DfromCalPlate3DAtPose_(i).translation.length is the        length of the translation component of the transformation        CalPlate3DfromCalPlate3DAtPose_(i);    -   CalPlate3DfromCalPlate3DAtPose_(i).rotationAngle is the rotation        amount of the transformation CalPlate3DfromCalPlate3DAtPose_(i)        (e.g., the rotation can be represented as a rotation amount        around a rotation axis); and    -   w is a weight (e.g., scale factor) for balancing the translation        and rotation components.

In some embodiments, the origin of Hand3D coordinate space 345 can beused as the basis for the cost function. A transformationHand3DFromHand3DAtPose_(i) can be defined as follows:Hand3DFromHand3DAtPose_(i)=Hand3DFromCamera3D*Camera3DFromCalPlate3DAtPose_(i)*CalPlate3DFromRobotBase3D*RobotBase3DFromHand3DAtPose_(i)

-   -   Where:    -   Hand3DFromCamera3D*Camera3DFromCalPlate3DAtPose_(i)*CalPlate3DFromRobotBase3D        represents the inverse of RobotBase3DFromHand3D observed by the        camera at pose i (Camera3DFromCalPlate3DAtPose_(i) is obtained        by using the observed features in Raw2D and camera calibration        information).        Hand3DFromHand3DAtPose_(i) indicates the difference between the        pose based on robot calibration parameters of robot 105 and the        estimated pose based on images from camera 110. If the        calibration parameters are completely accurate, then        Hand3DFromHand3DPose_(i) would be an identity transformation.        The cost function can be defined as follows:

$\sum\limits_{{{For}\mspace{14mu}{each}\mspace{14mu}{camera}},{{each}\mspace{14mu}{pose}\mspace{14mu} i},}\;\begin{pmatrix}{{{Hand}\; 3\; D\;{FromHand}\; 3\;{{DAtPose}_{i}.{translation}.{length}}} + {w*}} \\{{absolute}\mspace{14mu}{value}} \\( {{Hand}\; 3\;{DFromHand}\; 3\;{{DAtPose}_{i}.{rotation}.{angle}}} )\end{pmatrix}^{2}$

In some embodiments, the cost function can measure the differencebetween reported joint angles for the joints of robot 105 (e.g., asmeasured by robot 105) and the estimated joint angles of thecorresponding joints of robot 105. The cost function can estimate thejoint angles for the joints of robot 105 based on the captured imagesand the calibration parameter values. A transformationRobotBase3DFromHand3D_estimated can be defined as follows:RobotBase3DFromHand3D_estimated=RobotBase3DFromCalPlate3D*CalPlate3DFromCamera3DAtPose_(i)*Camera3DFromHand3D.

The inverse kinematic equations can be used to compute the joint anglescorresponding to RobotBase3DFromHand3D_estimated. The cost function canbe defined as follows:

$\sum\limits_{\underset{{each}\mspace{14mu}{joint}\mspace{14mu} j}{{{For}\mspace{14mu}{each}\mspace{14mu}{camera}},{{each}\mspace{14mu}{pose}\mspace{14mu} i}}}( {{EstimatedJointAngle} - {ReportedJointAngle}} )^{2}$  OR$\sum\limits_{\underset{{each}\mspace{14mu}{joint}\mspace{14mu} j}{{{For}\mspace{14mu}{each}\mspace{14mu}{camera}},{{each}\mspace{14mu}{pose}\mspace{14mu} i}}}( {{EstimatedJointEncoderCount} - {ReportedJointEncoderCount}} )^{2}$Beneficially, the cost function does not need to include w for balancingthe translation and rotation components.

4. Enhancing Refinement

In the illustrated example for machine vision system 100, thecalibration parameters that could be refined include 32 robotcalibration parameters: 20 D-H parameters for the joints of robot 105, 6robot calibration parameters for RobotBase3DFromJoint1, and 6 robotcalibration parameters for Joint6FromHand3D. The calibration parametersalso include 6 parameters for Camera3DFromHand3D, and 6 parameters forRobotBase3DFromCalPlate3D bringing the total number of calibrationparameters to 44 parameters.

There can be redundancy in the calibration parameters, making itunnecessary to refine all of the calibration parameters. In someembodiments, Joint6FromHand3D can be combined with Hand3DFromCamera3D toreduce the number of calibration parameters being refined. In someembodiments, RobotBase3DFromJoint1 can be combined withCalPlate3DFromRobotBase3D. Combining the transformations can reduce thecalibration parameters for refining to 32 (e.g., 6 fromCalPlate3DFromJoint1, 6 from Joint6FromCamera3D, and 20 fromJoint1FromJoint2, . . . , Joint5FromJoint6). In some embodiments, theD-H parameter θ offset and d offset from Joint1FromJoint2 can becombined into CalPlate3DFromJoint1, reducing the number of parametersfor refining to 30. In some embodiments, only select calibrationparameters are refined. For example, the offsets of the theta angles(e.g., the joint origins) can be refined. Beneficially, by reducing thenumber of calibration parameters for refining, the speed and accuracy ofrefining process can be improved. In some embodiments, refining can bedone in groups of calibration parameters. For example, the calibrationparameter values for Camera3DFromHand3D and RobotBase3DFromCalPlate3Dcan be fixed while refining the 20 robot calibration parameters. Then,the 20 robot calibration parameters can be fixed and the calibrationparameters for Camera3DFromHand3D and RobotBase3DFromCalPlate3D can berefined.

It should be appreciated that machine vision system 100 is an exemplarymachine vision system for practicing the technology. Otherconfigurations are contemplated. In some embodiments, steps described asperformed by the control system can be performed by a motion controller,a machine vision processor, and/or a motion controller in cooperationwith a machine vision processor. For example, a motion controller candirect the robot through a series of poses and cause the machine visionprocessor to acquire images of the calibration target at each pose. Themotion controller can provide to the machine vision processorinformation about the robot joint angles at each pose. The motioncontroller can cause the machine vision processor to perform thedescribed calibration and refinement. As another example, a machinevision processor can cause the motion controller to direct the robotthrough a series of poses and provide to the machine vision processorinformation about the robot joint angles at each pose. The machinevision processor can acquire images of the calibration target at eachpose. The machine vision processor can perform the described calibrationand refinement. More generally, the control system can comprise a motioncontroller, a machine vision processor, or any combination thereofworking in concert to implement the technology herein.

In some embodiments, more than one camera can be used. In such machinevision systems, the cost function can be the combination of the costfunctions for each camera. In some embodiments, a virtual 3D camera canbe created. By using a virtual 3D camera, a single camera-based costfunction can be used. Beneficially, by using a virtual 3D camera, thenumber of calibration parameters for refining can be smaller and thecameras' spatial relationship can be held constant during therefinement.

In some embodiments, multiple work spaces can be used (e.g., the robotcan move within and interact with objects in more than one work space).In implementations where the camera moves with the robot, thencalibration can include placing a calibration target in each workspaceand collecting calibration data (e.g., images and joint angles for aplurality of robot poses) for each workspace. Each additional workspacecan result in six additional calibration parameters for refining. Insome embodiments, the cost function can be the combination of costfunctions for each work space. In some embodiments, one or morestationary cameras can be used. If the one or more cameras arestationary, and the calibration target is mounted on the robot, then thecost functions defined above can be used by exchanging Camera3D andCalPlate3D in the equations. In some embodiments, the technology can beused for refining the calibration parameters for a machine vision systemin which the robot motion only moves in two dimensions. It should beappreciated that the cost functions can be changed to use only 2Dinformation. In such cases, due to the limitation of the robot motions,the number of robot calibration parameters for refinement can be reducedfor robust refinement.

B. Calibration for Machine Vision Systems with Motion Stages

It should be appreciated that the technology can refine calibrationparameters for machine vision systems including motion stages by usingapproaches similar to those described above. The technology can refinehand-eye calibration parameters and motion stage calibration parametersin a single refinement calculation.

FIG. 5 depicts calibration scheme 500 in accordance with the technology.In some embodiments, the calibration scheme can be used for fixed cameraconfigurations. For example, calibration scheme 500 can be used formachine vision system 200 of FIG. 2. In FIG. 5, the ovals representcoordinate spaces. FIG. 5 includes Home2D coordinate space 510, Stage2Dcoordinate space 515, CalPlate2D coordinate space 520, Camera2Dcoordinate space 525, and Raw2D coordinate space 530. Arrows betweenovals represent transformations between the illustrated coordinatespaces. The calibration parameter values used for the transformationscan be determined and refined, as described with respect to theillustrative calibration methods below.

In the illustrated example, Home2D coordinate space 510 can be thecoordinate space in which other coordinate spaces and theirrelationships are described. Home2D coordinate space 510 can beorthonormal and defined by the X axis of motion stage 205 and the centerof rotation of motion stage 205. For example, the origin of Home2Dcoordinate space 510 can be at its center of rotation when motion stage205 is at the home position. The x axis of Home2D coordinate space 510can be aligned with the x axis of motion stage 205. The y axis of Home2Dcoordinate space 510 can be 90 degrees from the X axis and in thegeneral direction of the y axis of motion stage 205. Stage2D coordinatespace 515 can be an orthonormal coordinate space that is attached to thecenter of rotation of motion stage 205, and moves along with motionstage 205. CalPlate2D coordinate space 520 can be the coordinate spaceof calibration target 220. This space can be moved around in the Home2Dcoordinate space 510 coordinates by motion stage 205. CalPlate2Dcoordinate space 520 can be an orthonormal coordinate system, althoughits length unit may have a non-identity scale factor from Home2Dcoordinate space 510. CalPlate2D coordinate space 520 and Home2Dcoordinate space 510 can have different handedness. Camera2D coordinatespace 525 can be the physical orthonormal coordinate space for camera210. The origin of Camera2D coordinate space 525 can be at a position inHome2D coordinate space 510 that corresponds to the center of the imagewindow of camera 210. Its x axis is parallel to the x axis of Raw2Dcoordinate space 530 at the origin of Camera2D coordinate space 525. They axis can be 90 degrees from the x axis and in the general direction ofthe y axis of Raw2D coordinate space 530. Raw2D coordinate space 530 canbe the pixel space coordinate system of camera 210.

The transformation between the coordinate spaces can be rigidtransformations (e.g., comprising a translation component and a rotationcomponent) and/or rigid plus handedness transforms (e.g. comprising arigid transform plus a handedness component) and/or transformationsbased on the kinematic calibration parameters of motion stage 205. Forexample, the transformations between Camera2D coordinate space 525 andHome2D coordinate space 510 and between Stage2D coordinate space 515 andCalPlate2D coordinate space 520 can be 2D rigid transformations. Thetransformations between CalPlate2D coordinate space 520 and Camera2Dcoordinate space 525 can be 2D rigid transformation. The transformationsbetween Home2D coordinate space 510 and Stage2D coordinate space 515 canbe based on, e.g., the actuators' encoder counts. The transformationfrom Camera2D coordinate space 525 to Raw2D coordinate space 530 can bebased on a conventional camera calibration, as is well known in the art.

1. Capturing Calibration Data

Again with reference to FIG. 4, the depicted method can be performed bycontrol system 215 of machine vision system 200. At step 405, controlsystem captures images and actuator encoder counts when motion stage 205is in a plurality of poses. At each pose, control system 215 causes thecamera to capture an image of at least a portion of calibration target220 that contains one or more features. Control system 215 furthercaptures the encoder count for each actuator of motion stage 2015 ateach pose.

2. Determining Initial Calibration Parameter Values

At step 410, control system 215 determines initial calibration parametervalues. The initial calibration parameter values can be the values usedto determine the transformations discussed with reference to FIG. 5prior to refinement. The values of these calibrations parameters can berefined in accordance with the present technology. In the illustratedexample of FIG. 4, control system 215 can obtain the initial motionstage calibration parameter values for motion stage 205 based on thespecification of motion stage 205. For example, a motion stagemanufacturer will typically provide these values. Using these initialcalibration values and the encoder counts at a particular pose, controlsystem 215 can determine the transformation Home2DFromStage2D.

Control system 215 can perform a hand-eye calibration to determineinitial hand-eye calibration parameter values. For example, controlsystem 215 can use the Cognex Vision Library to determine initialhand-eye calibration parameter values based on the captured images andthe Home2DFromStage2D transformation for a plurality of poses. As aresult of the hand-eye calibration, control system 215 can determineStage2DFromCalPlate2D, CalPlate2DFromCamera2D, and Camera2DfromHome2D.

3. Refining Calibration Parameters

At step 415, control system 215 refines a plurality of the calibrationparameters to determine more accurate values for those calibrationparameters. To refine the calibration parameters, control system 215determines the calibration parameters that minimize a cost function. Ingeneral, the cost functions can be based on comparing motion stage 205motions (e.g., as determined from the actual encoder counts read fromthe motion stage) and the observed camera or calibration target motions(e.g., based on the images captured by the camera). Embodiments of thetechnology can use a variety of cost functions.

In some embodiments, the cost function can measure the differencesbetween the observed encoder count (e.g., as read from the motion stage)and the expected/estimated encoder count as calculated using the initialcalibration parameter values (or successively refined calibrationparameter values). For example, for each motion stage poses i, anestimated motion stage pose i′ (e.g., in Home2D coordinate space 510)can be computed. Pose i′ can be computed as follows:Posei′=Home2DFromCamera2D*Camera2DFromCalPlate2DAtPose_(i)*Plate2DFromStage2D

-   -   Where Camera2DFromCalPlate2DAtPose_(i) is computed from image        features and the camera calibration information.

Estimated encoder counts for pose i can be computed based on pose i′ andthe initial calibration parameter values (or successively refinedcalibration parameter values).

The cost function can be the sum of the squares of encoder countdifferences for every actuator, for every pose, and for every camera (inmultiple camera machine vision systems). The cost function can bedefined as follows:

$\sum\limits_{\underset{camera}{{for}\mspace{14mu}{each}}}\;{\sum\limits_{\underset{{pose}\mspace{14mu} i}{{for}\mspace{14mu}{each}}}\;{\sum\limits_{\underset{{actuator}\mspace{14mu} j}{{for}\mspace{14mu}{each}}}\;( {{{Read}\mspace{14mu}{encoder}\mspace{14mu}{count}} - {{Estimated}\mspace{14mu}{encoder}\mspace{14mu}{count}}} )^{2}}}$

In some embodiments, the cost function can measure the differencesbetween the observed location of features in Raw2D and the expected(mapped) location of features in Raw2D. The transformationMappedFeatureRaw2D_(ij) can be defined as follows:MappedFeatureRaw2D_(ij)=Raw2DFromCamera2D*CalPlate2DFromCamera2DAtPose_(i)Estimated⁻¹*CalibrationTargetFeature_(j)whereCalPlate2DFromCamera2DAtPose_(i)Estimated=CalPlate2DFromStage2D*Home2DFromStage2DAtPose_(i)⁻¹*Home2DFromCamera2DHome2DFromStage2DAtPose_(i) can be computed based on the encoder countsread from motion stage 205 at pose i and the initial calibrationparameter values (or successively refined calibration parameter values).Control system 115 can then compute the distance between the observedfeature location and the mapped feature location. The cost function canbe defined as follows:

$\sum\limits_{\underset{{and}\mspace{14mu}{each}\mspace{14mu}{feature}\mspace{14mu} j}{{{For}\mspace{14mu}{each}\mspace{14mu}{camera}},{{each}\mspace{14mu}{pose}\mspace{14mu} i},}}\;( {{diatance}\begin{pmatrix}{{{ObservedFeatureRaw}\; 2\; D_{ij}},} \\{{MappedFeatureRaw}\; 2\; D_{ij}}\end{pmatrix}} )^{2}$

In some embodiments, the cost function can measure the differencesbetween the location of features in CalPlate2D and the mapped locationof features on calibration target 220. For example,Home2DFromStage2DAtPose_(i) can be computed based on the encoder countsread from motion stage 205 at pose i and the initial calibrationparameter values (or successively refined calibration parameter values).The transformation CalPlate2DFromCalPlate2DAtPose_(i) can be computed asfollows:CalPlate2DFromCalPlate2DAtPose_(i)=CalPlate2DFromStage2D*Home2DFromStage2DAtPose_(i)⁻¹*Home2DFromCamera2D*Camera2DFromPlate2DAtPose_(i)Where Home2DFromStage2DAtPose_(i) can be computed based on the encodercounts read from motion stage 205 at pose i and the initial calibrationparameter values (or successively refined calibration parameter values)Camera2DFromCalPlate2DAtPose_(i) is obtained by using the observedfeatures in Raw2D and camera calibration information.

The transformation CalPlate2DFromCalPlate2DAtPose_(i) can be used to mapcalibration target features at pose i. The cost function can then bedefined as follows:

$\sum\limits_{\underset{{cameracamera}\mspace{14mu}{ID}}{{for}\mspace{14mu}{each}}}\;{\sum\limits_{\underset{{pose}\mspace{14mu} i}{{for}\mspace{14mu}{each}}}\;{\sum\limits_{\underset{{feature}\mspace{14mu} j}{{for}\mspace{14mu}{each}}}\;( {{diatance}\begin{pmatrix}{{CalPlate}\; 2\; D\;{FromCalPlate}\; 2\;{DAtPose}_{i}*} \\{{{featureCalPlate}\; 2\; D_{j}},{{featureCalPlate}\; 2\; D_{j}}}\end{pmatrix}} )^{2}}}$

With respect to UVW motion stages, motion stage calibration parameterscan include, for each actuator, the actuator's roller's center position,the roller's radius, the actuator's direction, the actuator's step size,the actuator's home encoder count, and the actuator's striker plate'sdirection. In some embodiments, a subset of the UVW motion stage'smotion stage calibration parameters can be refined. For example, in someembodiments, the roller's radius is not refined. In some embodiments,the home encoder count is not refined. As noted above, refinementefficiency can be increased by reducing the number of calibrationparameters being refined. With respect to XY Theta motion stages, motionstage calibration parameters can include, for each of the X and Yactuators, the actuator's direction and the actuator's step size. Forthe theta actuator, motion stage calibration parameters can include theactuator's roller's center position, the roller's radius, and theactuator's striker plate's direction. In some embodiments, a subset ofthe XY Theta motion stage's motion stage calibration parameters can berefined. For example, in some embodiments, the roller's radius is notrefined.

It should be appreciated that machine vision system 200 is an exemplarymachine vision system for practicing the technology. Otherconfigurations are contemplated. In some embodiments, steps described asperformed by the control system can be performed by a motion controller,a machine vision processor, and/or a motion controller in cooperationwith a machine vision processor. For example, a motion controller candirect the motion stage through a series of poses and cause the machinevision processor to acquire images of the calibration target at eachpose. The motion controller can provide to the machine vision processorinformation about the motion stage at each pose. The motion controllercan cause the machine vision processor to perform the describedcalibration and refinement. As another example, a machine visionprocessor can cause the motion controller to direct the motion stagethrough a series of poses and provide to the machine vision processorinformation about the motion stage at each pose. The machine visionprocessor can acquire images of the calibration target at each pose. Themachine vision processor can perform the described calibration andrefinement. More generally, the control system can comprise a motioncontroller, a machine vision processor, or any combination thereofworking in concert to implement the technology herein.

In some embodiments, one or more stationary cameras can be used asdescribed above. If the one or more cameras are moving cameras, that isthe cameras are rigidly attached to the motion stage, and thecalibration target is stationary, then the cost functions defined abovecan be used by exchanging Camera2D and CalPlate2D in the equations.

The above-described techniques can be implemented in digital and/oranalog electronic circuitry, or in computer hardware, firmware,software, or in combinations of them. The implementation can be as acomputer program product, i.e., a computer program tangibly embodied ina machine-readable storage device, for execution by, or to control theoperation of, a data processing apparatus, e.g., a programmableprocessor, a computer, and/or multiple computers. A computer program canbe written in any form of computer or programming language, includingsource code, compiled code, interpreted code and/or machine code, andthe computer program can be deployed in any form, including as astand-alone program or as a subroutine, element, or other unit suitablefor use in a computing environment. A computer program can be deployedto be executed on one computer or on multiple computers at one or moresites.

Method steps can be performed by one or more processors executing acomputer program to perform functions of the technology by operating oninput data and/or generating output data. Method steps can also beperformed by, and an apparatus can be implemented as, special purposelogic circuitry, e.g., a FPGA (field programmable gate array), a FPAA(field-programmable analog array), a CPLD (complex programmable logicdevice), a PSoC (Programmable System-on-Chip), ASIP(application-specific instruction-set processor), or an ASIC(application-specific integrated circuit), or the like. Subroutines canrefer to portions of the stored computer program and/or the processor,and/or the special circuitry that implement one or more functions.

Processors suitable for the execution of a computer program include, byway of example, both general and special purpose microprocessors, andany one or more processors of any kind of digital or analog computer.Generally, a processor receives instructions and data from a read-onlymemory or a random access memory or both. The essential elements of acomputer are a processor for executing instructions and one or morememory devices for storing instructions and/or data. Memory devices,such as a cache, can be used to temporarily store data. Memory devicescan also be used for long-term data storage. Generally, a computer alsoincludes, or is operatively coupled to receive data from or transferdata to, or both, one or more mass storage devices for storing data,e.g., magnetic, magneto-optical disks, or optical disks. A computer canalso be operatively coupled to a communications network in order toreceive instructions and/or data from the network and/or to transferinstructions and/or data to the network. Computer-readable storagemediums suitable for embodying computer program instructions and datainclude all forms of volatile and non-volatile memory, including by wayof example semiconductor memory devices, e.g., DRAM, SRAM, EPROM,EEPROM, and flash memory devices; magnetic disks, e.g., internal harddisks or removable disks; magneto-optical disks; and optical disks,e.g., CD, DVD, HD-DVD, and Blu-ray disks. The processor and the memorycan be supplemented by and/or incorporated in special purpose logiccircuitry.

The above described techniques can be implemented in a distributedcomputing system that includes a back-end component. The back-endcomponent can, for example, be a data server, a middleware component,and/or an application server. The above described techniques can beimplemented in a distributed computing system that includes a front-endcomponent. The front-end component can, for example, be a clientcomputer having a graphical user interface, a web browser through whicha user can interact with an example implementation, and/or othergraphical user interfaces for a transmitting device. The above describedtechniques can be implemented in a distributed computing system thatincludes any combination of such back-end, middleware, or front-endcomponents.

The components of a computing system can be interconnected bytransmission medium, which can include any form or medium of digital oranalog data communication (e.g., a communication network). Transmissionmedium can include one or more packet-based networks and/or one or morecircuit-based networks in any configuration. Packet-based networks caninclude, for example, the Internet, a carrier internet protocol (IP)network (e.g., local area network (LAN), wide area network (WAN), campusarea network (CAN), metropolitan area network (MAN), home area network(HAN)), a private IP network, an IP private branch exchange (IPBX), awireless network (e.g., radio access network (RAN), Bluetooth, Wi-Fi,WiMAX, general packet radio service (GPRS) network, HiperLAN), and/orother packet-based networks. Circuit-based networks can include, forexample, the public switched telephone network (PSTN), a legacy privatebranch exchange (PBX), a wireless network (e.g., RAN, code-divisionmultiple access (CDMA) network, time division multiple access (TDMA)network, global system for mobile communications (GSM) network), and/orother circuit-based networks.

Information transfer over transmission medium can be based on one ormore communication protocols. Communication protocols can include, forexample, Ethernet protocol, Internet Protocol (IP), a Peer-to-Peer (P2P)protocol, Hypertext Transfer Protocol (HTTP), Session InitiationProtocol (SIP), a Global System for Mobile Communications (GSM)protocol, Universal Mobile Telecommunications System (UMTS), 3GPP LongTerm Evolution (LTE) and/or other communication protocols.

Comprise, include, and/or plural forms of each are open ended andinclude the listed parts and can include additional parts that are notlisted. And/or is open ended and includes one or more of the listedparts and combinations of the listed parts.

One skilled in the art will realize the technology may be embodied inother specific forms without departing from the spirit or essentialcharacteristics thereof. The foregoing embodiments are therefore to beconsidered in all respects illustrative rather than limiting of thetechnology described herein.

The technology has been described in terms of particular embodiments.The alternatives described herein are examples for illustration only andnot to limit the alternatives in any way. The steps of the technologycan be performed in a different order and still achieve desirableresults. Other embodiments are within the scope of the following claims.

What is claimed is:
 1. A machine vision system comprising: a robot; acamera; and a control system in communication with the robot and thecamera, the control system configured to: move the robot to a pluralityof poses, and for each pose of the plurality of poses: capture, with thecamera, an image of one or more features on a calibration target; andcapture a plurality of robot joint angles; obtain a plurality of initialvalues for a plurality of robot calibration parameters; determine aplurality of initial values for a plurality of hand-eye calibrationparameters based on the plurality of initial values for the plurality ofrobot calibration parameters, and the image and the plurality of robotjoint angles captured for each of the plurality of poses; determine aplurality of final values for the plurality of hand-eye calibrationparameters and a plurality of final values for the robot calibrationparameters by refining one or more of the plurality of hand-eyecalibration parameters and one or more of the plurality of robotcalibration parameters to minimize a cost function.
 2. The machinevision system of claim 1, wherein the control system is furtherconfigured to: use the plurality of final values for the plurality ofhand-eye calibration parameters and the plurality of final values forthe robot calibration parameters for a vision guided robot application.3. The machine vision system of claim 1, wherein the control system isfurther configured to: move the robot using the plurality of finalvalues for the robot calibration parameters.
 4. The machine visionsystem of claim 1, wherein the cost function measures, for each pose ofthe plurality of poses, a difference between an observed location of afeature in the image captured for the pose and an expected location ofthe feature, the expected location determined based on a first pluralityof values for the plurality of robot calibration parameters, a secondplurality of values for the plurality of hand-eye calibrationparameters, and the plurality of robot joint angles captured for thepose.
 5. The machine vision system of claim 1, wherein the cost functionmeasures, for each pose of the plurality of poses, a difference betweena composite transformation and an identity transformation, the compositetransformation being a composition of a first transformation from afirst coordinate space to a second coordinate space and a secondtransformation from the second coordinate space to the first coordinatespace, the first transformation and the second transformation determinedbased on a first plurality of values for the plurality of robotcalibration parameters, a second plurality of values for the pluralityof hand-eye calibration parameters, the plurality of observed featuresof the calibration target for the pose, and the plurality of robot jointangles captured for the pose.
 6. The machine vision system of claim 1,wherein the cost function measures, for each pose of the plurality ofposes, a difference between a robot joint angle of the plurality ofrobot joint angles captured for the pose and an estimated joint anglefor the pose, the estimated joint angle determined based on a firstplurality of values for the plurality of robot calibration parameters, asecond plurality of values for the plurality of hand-eye calibrationparameters, and the plurality of observed features of the calibrationtarget for the pose.
 7. The machine vision system of claim 1, whereinthe control system is further configured to minimize the cost functionusing non-linear least squares.
 8. The machine vision system of claim 1,wherein the control system is configured to refine less than all of theplurality of hand-eye calibration parameters and less than all of theplurality of robot calibration parameters.
 9. The machine vision systemof claim 1, wherein the plurality of robot calibration parameterscomprises Denavit-Hartenberg parameters for the robot.
 10. A machinevision system-implemented calibration method comprising: moving, by acontrol system, a robot to a plurality of poses, and for each pose ofthe plurality of poses: capturing, by a camera, an image of one or morefeatures on a calibration target; and capturing, by the control system,a plurality of robot joint angles; obtaining, by the control system, aplurality of initial values for a plurality of robot calibrationparameters; determining, by the control system, a plurality of initialvalues for a plurality of hand-eye calibration parameters based on theplurality of initial values for the plurality of robot calibrationparameters, and the image and the plurality of robot joint anglescaptured for each of the plurality of poses; determining, by the controlsystem, a plurality of final values for the plurality of hand-eyecalibration parameters and a plurality of final values for the pluralityof robot calibration parameters by refining one or more of the pluralityof hand-eye calibration parameters and one or more of the plurality ofrobot calibration parameters to minimize a cost function.
 11. The methodof claim 10, wherein the cost function measures, for each pose of theplurality of poses, a difference between an observed location of afeature in the image captured for the pose and an expected location ofthe feature, the expected location determined based on a first pluralityof values for the plurality of robot calibration parameters, a secondplurality of values for the plurality of hand-eye calibrationparameters, and the plurality of robot joint angles captured for thepose.
 12. The method of claim 10, wherein the cost function measures,for each pose of the plurality of poses, a difference between acomposite transformation and an identity transformation, the compositetransformation being a composition of a first transformation from afirst coordinate space to a second coordinate space and a secondtransformation from the second coordinate space to the first coordinatespace, the first transformation and the second transformation determinedbased on a first plurality of values for the plurality of robotcalibration parameters, a second plurality of values for the pluralityof hand-eye calibration parameters, the plurality of observed featuresof the calibration target for the pose, and the plurality of robot jointangles captured for the pose.
 13. The method of claim 10, wherein thecost function measures, for each pose of the plurality of poses, adifference between a robot joint angle of the plurality of robot jointangles captured for the pose and an estimated joint angle for the pose,the estimated joint angle determined based on a first plurality ofvalues for the plurality of robot calibration parameters, a secondplurality of values for the plurality of hand-eye calibrationparameters, and the plurality of observed features of the calibrationtarget for the pose.
 14. The method of claim 10, further comprisingminimizing the cost function using non-linear least squares.
 15. Themethod of claim 10, further comprising refining less than all of theplurality of hand-eye calibration parameters and less than all of theplurality of robot calibration parameters.
 16. The method of claim 10,wherein the plurality of robot calibration parameters comprisesDenavit-Hartenberg parameters for the robot.
 17. A machine vision systemcomprising: a motion stage; a camera; and a control system incommunication with the motion stage and the camera, the control systemconfigured to: move the motion stage to a plurality of poses, and foreach pose of the plurality of poses: capture, with the camera, an imageof one or more features on a calibration target; and capture a pluralityof encoder counts for a plurality of actuators of the motion stage;obtain a plurality of initial values for a plurality of motion stagecalibration parameters; determine a plurality of initial values for aplurality of hand-eye calibration parameters based on the plurality ofinitial values for the plurality of motion stage calibration parameters,and the image and the plurality of encoder counts captured for each ofthe plurality of poses; determine a plurality of final values for theplurality of hand-eye calibration parameters and a plurality of finalvalues for the motion stage calibration parameters by refining one ormore of the plurality of hand-eye calibration parameters and one or moreof the plurality of motion stage calibration parameters to minimize acost function.
 18. The machine vision system of claim 17, wherein thecontrol system is further configured to: use the plurality of finalvalues for the plurality of hand-eye calibration parameters and theplurality of final values for the motion stage calibration parametersfor a vision guided motion stage application.
 19. The machine visionsystem of claim 17, wherein the control system is further configured to:move the motion stage using the plurality of final values for the motionstage calibration parameters.
 20. The machine vision system of claim 17,wherein the cost function measures, for each pose of the plurality ofposes, a difference between an observed location of a feature in theimage captured for the pose and an expected location of the feature, theexpected location determined based on a first plurality of values forthe plurality of motion stage calibration parameters, a second pluralityof values for the plurality of hand-eye calibration parameters, and theplurality of encoder counts captured for the pose.
 21. The machinevision system of claim 17, wherein the cost function measures, for eachpose of the plurality of poses, a difference between an encoder count ofthe plurality of encoder counts captured for the pose and an estimatedencoder count for the pose, the estimated encoder count determined basedon a first plurality of values for the plurality of motion stagecalibration parameters, a second plurality of values for the pluralityof hand-eye calibration parameters, and the plurality of observedfeatures of the calibration target for the pose.
 22. The machine visionsystem of claim 17, wherein the control system is further configured tominimize the cost function using non-linear least squares.
 23. Themachine vision system of claim 17, wherein the control system isconfigured to refine less than all of the plurality of hand-eyecalibration parameters and less than all of the plurality of motionstage calibration parameters.
 24. The machine vision system of claim 17,wherein the plurality of motion stage calibration parameters comprisesone or more of roller center position, roller radius, direction, stepsize, home encoder count, and striker plate's direction for an actuator.25. A machine vision system-implemented calibration method comprising:moving, by a control system, a motion stage to a plurality of poses, andfor each pose of the plurality of poses: capture, by a camera, an imageof one or more features on a calibration target; and capturing, by thecontrol system, a plurality of encoder counts for a plurality ofactuators of the motion stage; obtaining, by the control system, aplurality of initial values for a plurality of motion stage calibrationparameters; determining, by the control system, a plurality of initialvalues for a plurality of hand-eye calibration parameters based on theplurality of initial values for the plurality of motion stagecalibration parameters, and the image and the plurality of encodercounts captured for each of the plurality of poses; determining, by thecontrol system, a plurality of final values for the plurality ofhand-eye calibration parameters and a plurality of final values for themotion stage calibration parameters by refining one or more of theplurality of hand-eye calibration parameters and one or more of theplurality of motion stage calibration parameters to minimize a costfunction.
 26. The method of claim 25, wherein the cost functionmeasures, for each pose of the plurality of poses, a difference betweenan observed location of a feature in the image captured for the pose andan expected location of the feature, the expected location determinedbased on a first plurality of values for the plurality of motion stagecalibration parameters, a second plurality of values for the pluralityof hand-eye calibration parameters, and the plurality of encoder countscaptured for the pose.
 27. The method of claim 25, wherein the costfunction measures, for each pose of the plurality of poses, a differencebetween an encoder count of the plurality of encoder counts captured forthe pose and an estimated encoder count for the pose, the estimatedencoder count determined based on a first plurality of values for theplurality of motion stage calibration parameters, a second plurality ofvalues for the plurality of hand-eye calibration parameters, and theplurality of observed features of the calibration target for the pose.28. The method of claim 25, further comprising minimizing the costfunction using non-linear least squares.
 29. The method of claim 25,further comprising refining less than all of the plurality of hand-eyecalibration parameters and less than all of the plurality of motionstage calibration parameters.
 30. The method of claim 25, wherein theplurality of motion stage calibration parameters comprises one or moreof roller center position, roller radius, direction, step size, homeencoder count, and striker plate's direction for an actuator.